Logic Gates

Two Input Logic Gates

For 2 logical inputs, there are 16 possible logic gates. Table 1 defines the 16 logic gates, shows logical symbol, behavior in symbolic logic, provides name, notes.

People are most familiar with the ones that are named: NAND, NOR, AND, OR, XOR. Table 1 includes these, as well as AND and OR gates with either input negated, logic 0 and logic 1(which aren't really logic gates), and some gates that aren't really binary.

  Output when AB is        
Gate # 00 01 10 11 Symbolic Logical Description Symbol Name/Description Note
0 0 0 0 0 0 Always zero Not really a gate
1 0 0 0 1 A & B AND  
2 0 0 1 0 A & ~B A and Not B Universal
3 0 0 1 1 A A Not BInary
4 0 1 0 0 ~A & B B and Not A Universal
5 0 1 0 1 B B Not Binary
6 0 1 1 0 (A & ~B) | (~A & B) XOR Also Not Equals Function
7 0 1 1 1 A | B OR
8 1 0 0 0 ~(A | B) NOR Universal
9 1 0 0 1 (A & B) | (~A & ~B) XNOR Also Equals Function
10 1 0 1 0 ~B Not B Not Binary
11 1 0 1 1 A | ~B A or Not B Universal
12 1 1 0 0 ~A Not A Not Binary
13 1 1 0 1 ~A | B B or Not A Unversal
14 1 1 1 0 ~(A & B) NAND Universal
15 1 1 1 1 1 Always 1 Not really a gate

Using a Universal Gate to Construct Other Gates

Examples (a)-(g) below demonstrate how one can use a universal gate (here, the NAND gate) to construct several other gates: